# Writing Limits

## Main Question or Discussion Point

so solving lim's can be tedious not because they are hard but because you have to continously keep writing lim x->a while solving the equation is there a mathematical shortcut to writing limits without keep writing lim x->a all the time after each development???

thanks.

UltrafastPED
Gold Member
You can develop your own private notation for your private notes ... for example just draw an underline, and make a note as to what it means.

• 1 person
You can develop your own private notation for your private notes ... for example just draw an underline, and make a note as to what it means.
i know, but i meant for the exam will => do the trick?

Office_Shredder
Staff Emeritus
Gold Member
On an exam you are likely to be expected to write $\displaystyle \lim_{x\to a}$ on every single line, unless you are actually writing something down which is not a limit. Your instructor's opinion may vary (you should ask them if you feel it's really important), but I find it unlikely. There are two reasons for this

1.) Writing six characters four or five times doesn't take that much time.
2.) A LOT of students don't understand what limit notation actually means, so instructors absolutely need to grade on correctness here.
3.) You should never write down things which are not mathematically true on an exam, and this is no exception.

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• 1 person
Mark44
Mentor
A significant amount of the work in evaluating a limit is manipulating the expression so that you can actually take the limit. For these preliminary steps, since you haven't taken the limit yet, it's important that you include the "lim x -> a" part.

• 1 person
HallsofIvy
Homework Helper
Quite frankly, if the hard part is writing the "$\lim_{x\to a}$" you must be brilliant- and painfully lazy!

If your algebra goes $\lim_{x\to a}f(x)=\lim_{x\to a}g(x)=\lim_{x\to a}h(x)=\lim_{x\to a}k(x)=L$, and if the above equality holds because $f=g=h=k$ everywhere, then you could do your algebra in two steps:
- $\forall x, \enspace f(x)=g(x)=h(x)=k(x)$.
- Therefore $\lim_{x\to a}f(x)=\lim_{x\to a}k(x)=M$.

• 1 person
Quite frankly, if the hard part is writing the "$\lim_{x\to a}$" you must be brilliant- and painfully lazy!
some of the lims get a bit complicated and keep writing lim x->a all the time like 10 times is a pain in the butt.

Mark44
Mentor
some of the lims get a bit complicated and keep writing lim x->a all the time like 10 times is a pain in the butt.
Then you can do it like economicsnerd suggests below.

If your algebra goes $\lim_{x\to a}f(x)=\lim_{x\to a}g(x)=\lim_{x\to a}h(x)=\lim_{x\to a}k(x)=L$, and if the above equality holds because $f=g=h=k$ everywhere, then you could do your algebra in two steps:
- $\forall x, \enspace f(x)=g(x)=h(x)=k(x)$.
- Therefore $\lim_{x\to a}f(x)=\lim_{x\to a}k(x)=M$.

HallsofIvy